Question

Calculate percentage error in determination of time period of a pendulum, if $T=2\pi \sqrt{\frac{l}{g}}$, where $l$ and $g$ are measured with $\pm 1$% and $\pm 2$% errors.

• A. $\pm 0.5$%
• B. $\pm 1.5$%
• C. $\pm 2.5$%
• D. $\pm 3$%

Answer 1

Answer: (B)

$\pm 1.5$%

$\frac{\Delta T}{T}\times 100=\pm (\frac{1}{2}\times \frac{\Delta l}{l}\times 100+\frac{1}{2}\times \frac{\Delta g}{g}\times 100)$
$=\pm (\frac{1}{2}\times 1+\frac{1}{2}\times 2)$
$=\pm 1.5$%